I've heard that when n is great enough a value, the sum of all values from binompdf within a bound can be approximated with normalcdf.
I wasn't paying enough during Stat yesterday, obviously (someone asked me to make a game on their calculator… I'm guilty), and now I don't understand the homework.
I understand how to use binompdf, but not binomcdf, and not how to approximate it with normalcdf…
Ex: Suppose that James guesses on each question of a 50 question true/false quiz. Find the probability that James passes if… passing is 25+ correct questions… passing is 30+ correct questions… and passing is 32+correct questions.
I eventually got the answers by using sum() and seq() in conjunction with binompdf(), but I'm positive that there's a simpler way to solve these problems using the other commands. I would know if I had paid attention in class yesterday, sorry.
Help, please?

Just to refresh my memory…
By summing the values of the binomial pdf, you get the binomial cdf (PDF = Probability Distribution Function, CDF= Cumulative Distribution Function). The binomial PDF given probability P, with N trials and K successes is given by :

(1)

\begin{align} {n \choose k} p^{k}(1-p)^{n-k} \end{align}

(So pk gives number of successes, (1-p)n-k gives number of failures, the n choose k gives the number of ways this can be done).

Thanks. Can you explain how something that is
B(n,p)
is
N(np,sqrt(np(1-p))) - (we use the standard deviation rather than the variance as the second argument in our class, unlike wikipedia)
?
I understand how the mean = np, but I don't understand the formula for the standard deviation.

I was worried I would have to try to type out the proof, but luckily I found a nicely done one here. I am not sure what level stats class you are in, though. I taught myself statistics for the AP exam and I learned bio-stats which, from what I hear is on par with most other statistics courses. However, mathematical statistics is by far much better, but more complicated. That was where I was first introduced to the notations used in that proof.